Thanks for pointing this out! We realized that if we consider an empty board an optimizing system then any finite pattern is an optimizing system (because it’s similarly robust to adding non-viable collections of live cells), which is not very interesting. We have updated the post to reflect this.
The ‘bottle cap’ example would be an optimizing system if it was robust to cells colliding / interacting with it, e.g. being hit by a glider (similarly to the eater).
We realized that if we consider an empty board an optimizing system then any finite pattern is an optimizing system (because it’s similarly robust to adding non-viable collections of live cells)
Ah. I interpreted the statement about the empty board as being one of:
A small random perturbation, will probably be non-viable/collapse back to the empty board. (Whereas patterns that are viable don’t (necessarily) have this property.)
I then, asked about whether the bottle cap example, had the same robustness.
Ah I see, thanks for the clarification! The ‘bottle cap’ (block) example is robust to removing any one cell but not robust to adding cells next to it (as mentioned in Oscar’s comment). So most random perturbations that overlap with the block will probably destroy it.
Thanks for pointing this out! We realized that if we consider an empty board an optimizing system then any finite pattern is an optimizing system (because it’s similarly robust to adding non-viable collections of live cells), which is not very interesting. We have updated the post to reflect this.
The ‘bottle cap’ example would be an optimizing system if it was robust to cells colliding / interacting with it, e.g. being hit by a glider (similarly to the eater).
Ah. I interpreted the statement about the empty board as being one of:
A small random perturbation, will probably be non-viable/collapse back to the empty board. (Whereas patterns that are viable don’t (necessarily) have this property.)
I then, asked about whether the bottle cap example, had the same robustness.
Ah I see, thanks for the clarification! The ‘bottle cap’ (block) example is robust to removing any one cell but not robust to adding cells next to it (as mentioned in Oscar’s comment). So most random perturbations that overlap with the block will probably destroy it.